Question

if A = {1,2,3,4} and R is a relation on itself such that R = {(1,1), (2,2), (3,3) } is R reflexive?

Answer 1

Do you have for every x in A we also have (x,x) is in R?

Answer 2

(4,4) isn't

Answer 3

in R

Answer 4

this question means
do you have (1,1), (2,2),(3,3),and (4,4)?
and you are right so it isn't reflexive

Answer 5

you have to have for all!!!!! x in A we have (x,x) is in R
That for all part being the key word.

Answer 6

oh I thought I only need to check those x in A that are in R

Answer 7

i think you are thinking of symmetry and transitive

because we don't have to have for all a,b in A that (a,b) and (b,a) is in R


the definition for symmetry is if you have (a,b) in R then you must have (b,a)

Answer 8

I see. thank you!

Answer 9

so if we define a relation R on A
that relation R being {(1,3),(3,1)}
R wouldn't be reflexive
R would be symmetric since we do have (1,3) but we also have (3,1)
R is also transitive
Remember if then statements are only false when you have true if and a false then.
But we couldn't find a case where the if part was true so we don't have to worry if our then part is true or false because our if then statement is true
I think they use the phrase "it is vacuously true"

Answer 10

lol i was gonna point that out

Answer 11

so if R = {(1,1)}
R is not reflexive
R is symmetric
R is transitive

correct?

Answer 12

totally

Answer 13

got it. Thanks ;)

Answer 14

just be careful with those if then statements
and you will have to recall your truth tables